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Properties of REAL Numbers

Properties of REAL Numbers. Opposites. Two real numbers that are the same distance from the origin of the real number line are opposites of each other. EXAMPLES -100 AND 100 2 AND -2. Reciprocals. Absolute Value. Commutative Property of Addition. a + b = b + a

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Properties of REAL Numbers

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  1. Properties of REAL Numbers

  2. Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other. EXAMPLES -100 AND 100 2 AND -2 www.numberbender.com

  3. Reciprocals www.numberbender.com

  4. Absolute Value www.numberbender.com

  5. Commutative Property of Addition a + b = b + a When adding two numbers, the order of the numbers does not matter. EXAMPLES 2 + 3 = 3 + 2 (-5) + 4 = 4 + (-5) www.numberbender.com

  6. Commutative Property of Multiplication a × b = b × a When multiplying two numbers, the order of the numbers does not matter. EXAMPLES 2 × 3 = 3 × 2 (-3) × 24 = 24 × (-3) www.numberbender.com

  7. Associative Property of Addition a + (b + c) = (a + b) + c When three numbers are added, it makes no difference which two numbers are added first. EXAMPLES 2 + (3 + 5) = (2 + 3) + 5 (4 + 2) + 6 = 4 + (2 + 6) www.numberbender.com

  8. Associative Property of Multiplication a(bc) = (ab)c When three numbers are multiplied, it makes no difference which two numbers are multiplied first. EXAMPLES 2 × (3 × 5) = (2 × 3) × 5 (4 × 2) × 6 = 4 × (2 × 6) www.numberbender.com

  9. Distributive Property a(b + c) = ab + ac Multiplication distributes over addition. EXAMPLES 2 (3 + 5) = (2 × 3) + (2 × 5) (4 + 2) × 6 = (4 × 6) + (2 × 6) www.numberbender.com

  10. Additive Identity Property The additive identity property states that if 0 is added to a number, the result is that number. EXAMPLE 3 + 0 = 0 + 3 = 3 www.numberbender.com

  11. Multiplicative Identity Property The multiplicative identity property states that if a number is multiplied by 1, the result is that number. EXAMPLE 5 × 1 = 1 × 5 = 5 www.numberbender.com

  12. Additive Inverse Property The additive inverse property states that opposites add to zero. EXAMPLE 7 + (-7) = 0 and -4 + 4 = 0 www.numberbender.com

  13. Multiplicative Inverse Property www.numberbender.com

  14. PRACTICE EXERCISES www.numberbender.com

  15. Identify which property justifies each of the following: 4 × (8 × 2) = (4 × 8) × 2 Associative Property of Multiplication www.numberbender.com

  16. Identify which property justifies each of the following: 6 + 8 = 8 + 6 COMMUTATIVE PROPERTY OF ADDITION www.numberbender.com

  17. Identify which property justifies each of the following: 12 + 0 = 12 ADDITIVE IDENTITY PROPERTY www.numberbender.com

  18. Identify which property justifies each of the following: 5(2 + 9) = (5 × 2) + (5 ×9) DISTRIBUTIVE PROPERTY www.numberbender.com

  19. Multiplicative Inverse Property www.numberbender.com

  20. Identify which property justifies each of the following: 5 × 24 = 24 ×5 Commutative Property of Multiplication www.numberbender.com

  21. Identify which property justifies each of the following: 18 + (-18) = 0 Additive Inverse Property www.numberbender.com

  22. Identify which property justifies each of the following: -34 × 1 = -34 Multiplicative Identity Property www.numberbender.com

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